Our Monte Carlo sampling strategy is based on data resampling methodology, whereby multiple maximum likelihood optimizations are carried out.
Each optimization consists of taking a random point in parameter space and fitting the parameters to data that have been distorted away from the central values by Gaussian shifts within the quoted uncertainties.
To build the Monte Carlo samples, we use the multi-step strategy developed in Ref. [1]}, where the PDF and FF parameters are pre-optimized to minimize evaluating the likelihood in parameter regions that are strongly disfavored.
To that end we start by first considering PDF and FF parameters separately using flat priors, with the resulting samples from each type of hadron structure combined at a later stage to build new prior samples for the final runs.
The workflow is illustrated in Fig. REF , where each step is represented as vertical arrows that accumulate additional experimental data from the previous step, with the posterior samples at each step becoming the priors for the subsequent step.
This strategy allows the samples to become more optimized and avoids unnecessary likelihood evaluations in regions of parameters space by disfavoring those regions in earlier stages of the multi-step chain.
